Beth read 1 in 3 of the original pages, and then Beth reads 1 in 4 of them again.

So, if she read 2403=80 pages originally, she now reads 20 of those same pages again.

The same will be true for Carolyn and George, so 3 × 20 pages = 60 pages will be read by the same person when the book is re-read with the help of Sam.

4. How does the sun shine?

Derek Muller from YouTube’s Veritasium channel asks people to explain the mechanism that is responsible for the sun shining. Have a think yourself before you watch Derek explain the physics behind sunshine.

5. Junior Maths Challenge UKMT bonus

As the Junior Maths Challenge is now not far away, here is a bonus (and particularly tough) JMC question to stretch your brain.

3 marks

5.1. After playing 500 games, my success rate at Spider Solitaire is 49%. Assume that I now lose every third game, so that after 500 games my results are Win, Win, Loss, Win, Win, Loss, … .

What is the least number of extra games I need to play in order that my success rate becomes at least 50%?

Correct Solution: 26

Since I have won 49% of my first 500 games, so far I have won:

49100×500=49×5=245 games.

So I have lost 500–245=255 games. I need now to win enough games so that I have won as many as I have lost.

So, assuming I win 2 out of 3 games from now on, I get the following pattern:

# games

Wins

Losses

500

245

255

503

247

256

506

249

257

509

251

258

512

253

259

515

255

260

518

257

261

521

259

262

524

261

263

527

263

264

530

265

265

So, it would be easy to assume that I need to play 30 more games, so that the number of wins equals the number of losses. However, let’s take a closer look at what happens towards the end, bearing in mind the win-win-loss pattern.

# games

Wins

Losses

524

261

263

525

262

263

526

263

263

527

263

264

528

264

264

529

265

264

530

265

265

So, the number of wins equals the number of losses three times – after 526, 528 and 530 games. Therefore, the earliest that the number of wins equals the number of loses is after 526 games, or after 26 more games.

6. Rattleback

Watch this video of one of the most mysterious objects in the universe. It’s called a rattleback, and you can win one if you succeed at the challenge in the Additional Stuff section below.

Make sure you go through the solution sheet – it is massively important.

A score of less than 50% is ok – it means you can learn lots from your mistakes.

The next Parallelogram is next week, at 3pm on Thursday.

Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio,
Simon.

Additional Stuff

VAX! – a game about epidemic prevention.

Take a look at the game on the VAX! website, which is all about showing how maths can help reduce the spread of disease. We are all connected to each other and it is through these connections that diseases spread. You can reduce the spread of disease by breaking these connections, either by vaccinating people or putting them in quarantine.

It is definitely worth looking at the whole site and learning about the maths of disease, networks and connections, but if you want to jump straight in to the game then this is how to find it and how to win a rattleback.

If you would like to win a rattleback, then please send us your best VAX! score. The top three scores received by 12pm on Tuesday 19th March will win a rattleback. Just email me at prizes@parallel.org.uk and include an image of your bar chart score. Good luck.